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 A299705 Number of ways to dissect an equilateral triangle into n non-overlapping equilateral triangles counting isomorphisms only once. 3
 1, 0, 0, 1, 0, 1, 2, 3, 9, 23, 62, 188, 574, 1826, 5953, 19664, 66049, 224700, 771859, 2674753 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS Data from Figure 7 of Drapal and Hamalainen, see link. LINKS Ales Drapal, Carlo Hamalainen, An enumeration of equilateral triangle dissections, arXiv:0910.5199 [math.CO], 2009-2010. Hugo Pfoertner, Rainer Rosenthal, Illustration of the 23 dissections into 10 triangles. EXAMPLE a(9)=9:         *                 *                              *        / \               / \                            / \       *---*             +   +                          +   +      / \ / \           /     \                        /     \     *---*---*         +       +                      +       +    / \ / \ / \       /         \                    /         \   *---*---*---*     +           +                  +           +                    /             \                /             \                   *---+---*---+---*              *---+---+---*---*                  / \     / \     / \            / \         / \ / \                 +   +   +   +   +   +          +   +       *---*---*                /     \ /     \ /     \        /     \     / \     / \               +       *---*---*       +      +       +   +   +   +   +              /         \ / \ /         \    /         \ /     \ /     \             *---+---+---*---*---+---+---*  *---+---+---*---+---*---+---* .               *         *---+---+---*---+---+---*         *              / \         \         / \         /         / \             +   +         +       +   +       +         +   +            /     \         \     /     \     /         /     \           +       +         +   *---*---*   +         +       +          /         \         \ / \ / \ / \ /         /         \         +           +         *---*---*---*         +           +        /             \         \         /         /             \       *---+---*---+---*         +       +         *---+---*---*---*      / \     / \     / \         \     /         / \     / \ / \ / \     +   +   +   +   *---*         +   +         +   +   +   *---*   +    /     \ /     \ / \ / \         \ /         /     \ /     \ /     \   *---+---*---+---*---*---*         *         *---+---*---+---*---+---* .               *         *---+---*---*---*---+---*         *              / \         \     / \ / \ / \     /         / \             +   +         +   +   *---*   +   +         +   +            /     \         \ /     \ /     \ /         /     \           *---*---*         *---+---*---+---*         +       +          / \ / \ / \         \             /         /         \         *---*---*---*         +           +         *---+---+---*        / \         / \         \         /         / \         / \       +   +       +   +         +       +         +   +       +   +      /     \     /     \         \     /         /     \     /     \     +       +   +       +         +   +         *---*---*   +       +    /         \ /         \         \ /         / \ / \ / \ /         \   *---+---+---*---+---+---*         *         *---*---*---*---+---+---* CROSSREFS Cf. A167123, A290697, A290821. Sequence in context: A298407 A227252 A274495 * A318231 A242271 A056198 Adjacent sequences:  A299702 A299703 A299704 * A299706 A299707 A299708 KEYWORD nonn,hard,more AUTHOR Peter Munn and Hugo Pfoertner, Feb 17 2018 EXTENSIONS Offset changed, also name to accommodate, following suggestion by M. F. Hasler, Feb 23 2018 STATUS approved

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Last modified April 18 19:31 EDT 2021. Contains 343089 sequences. (Running on oeis4.)